Question

If tan A +cot A =4, then $ta{n}^{4}A+co{t}^{4}A$ is equal to

• A. 110
• B. 191
• C. 80
• D. 194

Answer 1

The correct option is D

194

194

We have:

tan A +cot A =4

Squaring both sides

$(tanA+cotA{)}^2=4^2$

$\Rightarrow ta{n}^{2}A+co{t}^{2}A+2\left(tana\right)\left(cotA\right)=16$

$\Rightarrow ta{n}^{2}A+co{t}^{2}A=14$

squaring both the sides again:

$(ta{n}^{2}A+co{t}^{2}A{)}^2={14}^2$

$\Rightarrow ta{n}^{4}A+co{t}^4+2\left(ta{n}^{2}A\right)\left(co{t}^{2}A\right)=196$

$\Rightarrow ta{n}^{4}A+co{t}^{4}A=194$